First, work expands to the time you schedule for it. If you schedule a two hour meeting, you're likely to fill that two hours and waste valuable work time.

Second, 15 minutes is more than enough time if the meeting has a purpose, tasks are made and assigned, and you keep computers and phones out of the meeting room.

The best reason for a 15 minute meeting, however, is because of our attention spans and brain limits. Carmine Gallo, a professional coach and trainer, wrote on Linkedin about the reason TED talks are only allowed to be 18 minutes long:

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As the brain takes in new information and is forced to process it, millions of neurons are firing at once, burning energy and leading to fatigue and exhaustion. Researchers at Texas Christian University are finding that the act of listening can be as equally draining as thinking hard about a subject. Dr. Paul King calls it "cognitive backlog." Like weights, he says, the more information we are asked to take in, the heavier and heavier it gets. Eventually, we drop it all, failing to remember anything we've been told. In King's own research, he found that graduate students recall more of the information they learn when they go to class three days a week for 50 minutes instead of one day a week for three hours. Although most students say they'd prefer to get the class over with at once, they retain more information when receiving the information in shorter amounts of time.

Not every meeting may be able to be done in 15 minutes, but for the general day to day stuff there's no reason to be wasting away for hours while nothing is accomplished. If you need a little help, try setting a 15 minute timer and when it goes off, meeting is done.